Simplify the following expression and state the condition under which the simplification is valid: $y = \dfrac{p^2 + 7p}{p^2 - 2p - 63}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{p^2 + 7p}{p^2 - 2p - 63} = \dfrac{(p)(p + 7)}{(p - 9)(p + 7)} $ Notice that the term $(p + 7)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(p + 7)$ gives: $y = \dfrac{p}{p - 9}$ Since we divided by $(p + 7)$, $p \neq -7$. $y = \dfrac{p}{p - 9}; \space p \neq -7$